Nonlinear BLOCH-wave interaction and bragg scattering in optically induced lattices

We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.     

The structure of poly(ethylene oxide)8: NaBPh4 from a single crystal oligomer and polycrystalline polymer

We show that the structure of a polymer electrolyte may be solved by growing single crystals of an oligomeric (short chain) complex which provided an adequate starting model for refinement of the equivalent polymeric structure using powder diffraction: the efficacy of this method has been demonstrated by determining for the first time the structure of an 8 : 1 complex, poly(ethylene oxide)(8) : NaBPh(4).     

A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence

We study the two-dimensional gauge theory of the symmetric group S_n describing the statistics of branched n-coverings of Riemann surfaces. We consider the theory defined on the disc and on the sphere in the large-n limit. A non trivial phase structure emerges, with various phases corresponding to different connectivity properties of the covering surface. We show that any gauge theory on a two-dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold: in the case of S_n, one of the phase transitions we find can be interpreted as a cutoff phenomenon in the corresponding random walk. A connection with the theory of phase transitions in random graphs is also pointed out. Finally we discuss how our results may be related to the known phase transitions in Yang-Mills theory. We discover that a cutoff transition occurs also in two dimensional Yang-Mills theory on a sphere, in a large N limit where the coupling constant is scaled with N with an extra logN compared to the standard t Hooft scaling.     

Development of the force field parameters for phosphoimidazole and phosphohistidine

Phosphorylation of histidine-containing proteins is a key step in the mechanism of many phosphate transfer enzymes (kinases, phosphatases) and is the first stage in a wide variety of signal transduction cascades in bacteria, yeast, higher plants, and mammals. Studies of structural and dynamical aspects of such enzymes in the phosphorylated intermediate states are important for understanding the intimate molecular mechanisms of their functioning. Such information may be obtained via molecular dynamics and/or docking simulations, but in this case appropriate force field parameters for phosphohistidine should be explicitly defined. In the present article we describe development of the GROMOS96 force field parameters for phosphoimidazole molecule--a realistic model of the phosphohistidine side chain. The parameterization is based on the results of ab initio quantum chemical calculations with subsequent refinement and testing using molecular mechanics and molecular dynamics simulations. The set of force constants and equilibrium geometry is employed to derive force field for the phosphohistidine moiety. Resulting parameters and topology are incorporated into the molecular modeling package GROMACS and used in molecular dynamics simulations of a phosphohistidine-containing protein in explicit solvent.     

Nucleophilic displacement at benzhydryl centers: asymmetric synthesis of 1,1-diarylalkyl derivatives

[reaction: see text] Activation of substituted 1,1-diarylmethanols as their corresponding toluenesulfonates and subsequent displacement with a range of carbon, nitrogen, oxygen, and sulfur nucleophiles proceeds in 81-96% yield. Enantiomerically enriched diarylmethanols 8a-c were activated and displaced with pyridine acetate enolate with complete stereochemical inversion at carbon to yield 1,1-diarylalkyl derivatives 10a-c without loss of optical purity.     

Generating ultralow-emittance ion beams in a storage ring

Laser cooling of heavy-ion beams in a storage ring is systematically studied with a multiparticle simulation code where not only exact lattice characteristics and space-charge forces but also realistic laser-ion interactions can be incorporated. The resonant coupling method is applied in order to extend the powerful longitudinal photon pressure to the transverse degrees of freedom. It is shown that, in spite of a space-charge-induced tune shift, the synchrobetatron resonance mechanism required for fast damping of transverse oscillations operates throughout the cooling process. Extremely efficient three-dimensional cooling of stored ion beams is thus feasible. It is demonstrated that, at low line density, normalized root-mean-squared emittances of the order of 10(-12) m.rad can be reached in all three directions by employing only existing technologies.     

On the Arithmetic of Del Pezzo Surfaces of Degree 2

We study the arithmetic of certain del Pezzo surfaces of degree2. We produce examples of Brauer-Manin obstruction to the Hasseprinciple, coming from 2- and 4-torsion elements in the Brauergroup. 2000 Mathematics Subject Classification 14G05 (primary),12G05 (secondary).     

On a Theorem of Høegh-Krohn

A theorem proved by R. Høegh-Krohn in Comm. Math. Phys. 38(1974), 195–224, which yields a possibility to define states of systems of quantum particles by their values on the products , where \mathfraka _t , t are time automorphisms and F _j are multiplication operators, is generalized and extended. In particular, it is shown that the algebras generated by such products with F _j taken from the families of multiplication operators satisfying certain conditions are dense in the algebras of observables in the -weak topology, in which normal states are continuous. This result was obtained for the systems with two types of kinetic energy: the usual one expressed by means of the Laplacian; the relativistic kinetic energy defined by a pseudo-differential operator.     

Potentiometric and theoretical studies of the carbonate sensors based on 3-bromo-4-hexyl-5-nitrotrifluoroacetophenone

Novel carbonate ionophore, trifluoroacetophenone derivative (TFA) substituted by two acceptor substituents in the phenyl ring (3-bromo-4-hexyl-5-nitrotrifluoroacetophenone), was synthesized. Solvent polymeric membrane sensors based on this ionophore exhibited heightened selectivity to carbonate ions in the presence of the most important interfering anions. A wide range of potentiometric properties were studied and compared with those of sensors based on mono-substituted ionophores. Special attention was paid to pH dependence of sensor responses and to elaboration of appropriate conditions for carbonate analysis. A segmented-sandwich membrane method was applied for determination of the stoichiometry of ionophore-carbonate complexes, which was determined to be 1:3, and apparent complex formation constants which were 14.4 and 13.6 for DOS- and NPOE-plasticized membranes, respectively. Theoretical studies on TFA derivatives by semi-empirical (AM1 and PM3) and ab initio(6-31+G*) methods were performed, considering different types of possible ionophore-ion interactions. The formation of hydrogen bonds between carbonate and hydrated TFA was proved to be much more favourable in terms of energy compared to tetrahedral nucleophilic adducts that earlier were postulated to being formed in the membrane phase. The final conclusion on the mechanism of carbonate sensing by TFA-based solvent polymeric membrane sensors was made on the basis of computational data and detailed analysis of the literature.